Math / Algebra

QuestionGraph this function: $f(x)=\frac{4}{7} x-3$
Click to select points on the graph. Submit

Studdy Solution

STEP 1

1. The function $f(x) = \frac{4}{7}x - 3$ is a linear function.
2. We need to graph this function by identifying key points.

STEP 2

1. Identify the slope and y-intercept of the function.
2. Determine the y-intercept point.
3. Use the slope to find another point on the graph.
4. Plot the points and draw the line.

STEP 3

Identify the slope and y-intercept from the function $f(x) = \frac{4}{7}x - 3$ .
The slope $m$ is $\frac{4}{7}$ .
The y-intercept $b$ is $-3$ .

STEP 4

Determine the y-intercept point.
The y-intercept occurs when $x = 0$ .
Substitute $x = 0$ into the function:
$f(0) = \frac{4}{7}(0) - 3 = -3$
The y-intercept point is $(0, -3)$ .

STEP 5

Use the slope to find another point on the graph.
Starting from the y-intercept $(0, -3)$ , apply the slope $\frac{4}{7}$ .
This means for every increase of 7 units in $x$ , $y$ increases by 4 units.
From $(0, -3)$ , move 7 units to the right (increase $x$ by 7) and 4 units up (increase $y$ by 4).
The new point is $(7, 1)$ .

STEP 6

Plot the points $(0, -3)$ and $(7, 1)$ on the graph.
Draw a straight line through these points to represent the function.
The graph of the function $f(x) = \frac{4}{7}x - 3$ is now plotted with the points $(0, -3)$ and $(7, 1)$ .

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QuestionGraph this function: $f(x)=\frac{4}{7} x-3$
Click to select points on the graph. Submit

Studdy Solution

STEP 1

1. The function $f(x) = \frac{4}{7}x - 3$ is a linear function.
2. We need to graph this function by identifying key points.

STEP 2

1. Identify the slope and y-intercept of the function.
2. Determine the y-intercept point.
3. Use the slope to find another point on the graph.
4. Plot the points and draw the line.

STEP 3

Identify the slope and y-intercept from the function $f(x) = \frac{4}{7}x - 3$ .
The slope $m$ is $\frac{4}{7}$ .
The y-intercept $b$ is $-3$ .

STEP 4

Determine the y-intercept point.
The y-intercept occurs when $x = 0$ .
Substitute $x = 0$ into the function:
$f(0) = \frac{4}{7}(0) - 3 = -3$
The y-intercept point is $(0, -3)$ .

STEP 5

STEP 6

Plot the points $(0, -3)$ and $(7, 1)$ on the graph.
Draw a straight line through these points to represent the function.
The graph of the function $f(x) = \frac{4}{7}x - 3$ is now plotted with the points $(0, -3)$ and $(7, 1)$ .

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QuestionGraph this function: f(x)=47x−3f(x)=\frac{4}{7} x-3f(x)=74​x−3Click to select points on the graph. Submit

Studdy Solution

STEP 1

1. The function f(x)=47x−3 f(x) = \frac{4}{7}x - 3 f(x)=74​x−3 is a linear function.2. We need to graph this function by identifying key points.

STEP 2

1. Identify the slope and y-intercept of the function.2. Determine the y-intercept point.3. Use the slope to find another point on the graph.4. Plot the points and draw the line.

STEP 3

Identify the slope and y-intercept from the function f(x)=47x−3 f(x) = \frac{4}{7}x - 3 f(x)=74​x−3.The slope m m m is 47 \frac{4}{7} 74​.The y-intercept b b b is −3-3−3.

STEP 4

Determine the y-intercept point.The y-intercept occurs when x=0 x = 0 x=0.Substitute x=0 x = 0 x=0 into the function: f(0)=47(0)−3=−3 f(0) = \frac{4}{7}(0) - 3 = -3 f(0)=74​(0)−3=−3The y-intercept point is (0,−3) (0, -3) (0,−3).

STEP 5

STEP 6

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QuestionGraph this function: $f(x)=\frac{4}{7} x-3$
Click to select points on the graph. Submit

1. The function $f(x) = \frac{4}{7}x - 3$ is a linear function.
2. We need to graph this function by identifying key points.

1. Identify the slope and y-intercept of the function.
2. Determine the y-intercept point.
3. Use the slope to find another point on the graph.
4. Plot the points and draw the line.

Identify the slope and y-intercept from the function $f(x) = \frac{4}{7}x - 3$ .
The slope $m$ is $\frac{4}{7}$ .
The y-intercept $b$ is $-3$ .

Determine the y-intercept point.
The y-intercept occurs when $x = 0$ .
Substitute $x = 0$ into the function:
$f(0) = \frac{4}{7}(0) - 3 = -3$
The y-intercept point is $(0, -3)$ .